报告题目：双曲守恒律方程的Hermite WENO方法

（Hermite WENO schemes for hyperbolic conservation laws）

报 告 人：邱建贤 教授 厦门大学数学科学学院
报告时间：2017年10月15日（星期日）下午16：00-17：00

报告地点：文理楼254

报告人简介：邱建贤，博士，厦门大学闽江学者特聘教授，入选福建省第四批“百人计划”，国际著名刊物“J. Comp. Phys.” (计算物理) 编委。从事计算流体力学及微分方程数值解法的研究工作，在间断Galerkin（DG）、加权本质无振荡（WENO）数值方法的研究及其应用方面取得了一些重要成果，已发表论文七十多篇。主持国家自然科学基金重点项目和联合基金重点支持项目, 参与欧盟第六框架特别研究项目,是项目组中唯一非欧盟的成员。论文被引一千五百多次。多次被邀请在国际会议上作大会报告。 福建省数学建模与高性能计算重点实验室常务副主任, 中国计算数学学会常务理事, 福建省数学学会常务理事。

报告摘要：In this presentation, a class of high-order weighted essentially non-oscillatory (WENO) schemes based on Hermite polynomials, termed HWENO (Hermite WENO) schemes, for solving nonlinear hyperbolic conservation law systems is presented. The construction of HWENO schemesvis based on a finite volume formulation, Hermite interpolation, and nonlinearly stable Runge-Kutta methods. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and used in the reconstruction, while only the function values are evolved and used in the original WENO schemes. Comparing with the original WENO schemes of Liu et al. [J. Comput. Phys. 115 (1994) 200] and Jiang and Shu [J. Comput. Phys. 126 (1996) 202], one major advantage of HWENO schemes is its compactness in the reconstruction. For example, five points are needed in the stencil for a fifth-order WENO (WENO5) reconstruction, while only three points are needed for a fifth-order HWENO (HWENO5) reconstruction in one dimensional case. Numerical results are presented for both one and two dimensional cases to show the efficiency of the schemes.

理学院  科技处

2017-10-13